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[Display omitted] • Equivalence between continuous- and discrete-time models of optical flow sensor. • Optical flow sensor's calibration method via in-situ rotation. • Unmanned aerial vehicle position estimation algorithm based on optical flow sensor. To better reveal the principle of off-the-shelf OFS that used for UAV position estimation, two measurement models are derived, namely the continuous-time and discrete-time models. Then the intrinsic equivalence of these two models is also proven. Based on these two models, a calibration method for OFS is introduced, which only makes use of in-situ rotation to determine the OFS's parameters including its focal length and installation angles with respect to the UAV. Furthermore, an OFS-based UAV position estimation algorithm is presented, which stems from the proposed discrete-time model. The proposed OFS models, calibration method, and position estimation algorithm form a full solution for UAV displacement measurement via OFS, and its feasibility and effectiveness is verified through flight tests on a quadcopter UAV in outdoor environment. [ABSTRACT FROM AUTHOR]